A procedure has been developed for refinement of plausible starting models by addition of sparse experimental data. The method is demonstrated for determining the structure of E.Coli tRNAVal, originally modeled after the X-ray structure of yeast tRNAPhe, but refined using experimental residual dipolar coupling (RDC) and small angle X-ray scattering (SAXS) data. A spherical sampling algorithm has been developed for refinement against SAXS data that does not require a globbic approximation, which is particularly important for nucleic acids where such approximations are less appropriate. Substantially higher speed of the algorithm also makes its application favorable for proteins. In addition to the SAXS data, the structure refinement employed a sparse set of NMR data consisting of 24 imino N-HN RDCs measured with Pf1 phage alignment, and 20 imino N-HN RDCs obtained from magnetic field dependent alignment of tRNAVal. The refinement strategy aims to largely retain the local geometry of the 58% identical tRNAPhe by ensuring that the atomic coordinates for short, overlapping segments of the ribose-phosphate backbone and the conserved base pairs remain close to those of the starting model. Local coordinate restraints are enforced using the non-crystallographic symmetry (NCS) term in the XPLOR-NIH or CNS software package, while still permitting modest movements of adjacent segments. The RDCs mainly drive the relative orientation of the helical arms, whereas the SAXS restraints ensure an overall molecular shape compatible with experimental scattering data. The resulting structure exhibits good cross-validation statistics (jack-knifed Qfree = 14% for the Pf1 RDCs, compared to 25% for the starting model) and exhibits a larger angle between the two helical arms than observed in the X-ray structure of tRNAPhe, in agreement with previous NMR-based tRNAVal models. Inclusion of residual chemical shift anisotropy (CSA) as a complementary source of structural restraint hinges on accurate knowledge of the static CSA tensor for imino 15N resonances. The magnitude and orientation of the CSA tensors has been determined for both A and G nucleotides, using the structure of tRNA_Val as a reference point. Knowledge of the CSA values is also key to determining the dynamic properties of the nucleobases, a subject currently under investigation.